Question

The area of the circular base of a cylinder is 36π square units. The height of the cylinder is 2 units.

What is the lateral area of the cylinder? Express the answer in terms of π.

12π square units
24π square units
60π square units
72π square units

Answer 1

To find the lateral area of the cylinder, we need to use the formula for the lateral surface area of a cylinder, which is given by:

\[
\text{Lateral Area} = 2 \pi r h
\]

where \( r \) is the radius of the base of the cylinder and \( h \) is the height.

We know the area of the circular base of the cylinder is \( 36\pi \) square units. The area \( A \) of a circle is given by:

\[
A = \pi r^2
\]

Setting this equal to the area of the base:

\[
\pi r^2 = 36\pi
\]

We can simplify this by dividing both sides by \( \pi \):

\[
r^2 = 36
\]

Taking the square root of both sides gives us:

\[
r = 6
\]

Now, we know that the height \( h \) of the cylinder is 2 units. We can substitute \( r \) and \( h \) into the lateral area formula:

\[
\text{Lateral Area} = 2 \pi (6) (2)
\]

Calculating this gives:

\[
\text{Lateral Area} = 2 \pi \cdot 6 \cdot 2 = 24\pi
\]

Thus, the lateral area of the cylinder is:

\[
\boxed{24\pi} \text{ square units}
\]